This is a new answer to an old question, but I still think it's worthwhile to answer. There are a few ways to transplant the Ability Sturdy on to Shedinja, but most of them are extremely improbable to succeed. The most efficient one, however, is possible to complete in 2 turns. You need an extremely specific team in Triple Battles in order to pull it off.
The lynchpin of the operation is a Carpink with its Hidden Ability, Sturdy, and the move Skill Swap. The helping hand will come from a Pokemon with access to Thunder Wave, and a move that suppresses or changes the target's Ability (Worry Seed, Gastro Acid, etc). Prepare your team so that Shedinja is between them, as both will need to be able to target Shedinja for this to work. It is also highly recommended that you manipulate the natures and EVs of both Carbink and the other Pokemon, so that Carbink is 1 point of Speed slower than the other. This makes it as sure as possible that the ability suppressor will go first, and then Carbink will go immediately after it. This is important to minimize the amount of time in which Shedinja has no ability, and is basically floating there, naked, with no protection at all. Finally, give your Shedinja the Safety Goggles, to protect it from Hail and Sandstorm, as Wonder Guard only affects direct damage.
Turn 1, the other supporting Pokemon uses its Ability manipulation move on Shedinja to override or suppress Wonder Guard. This will allow Carbink to successfully use Skill Swap on Shedinja, giving Shedinja Sturdy. As long as Shedinja wasn't targeted before this point, you've completed the transaction.
Turn 2 we embellish on this, by using Thunder Wave on Shedinja. This prevents Shedinja from becoming Burned, Poisoned, or afflicted with Toxic.
But there's one other threat to a Sturdy Shedinja that you'd be well served in defending against, and that's Leech Seed. Like Sand, Hail, Burn, and Poison, Leech Seed's damage is indirect, and as such will not be affected by Sturdy. But Leech Seed has no effect on Grass types. We can add Grass type to Shedinja with another supporting status move, Forest's Curse. Make sure a Pokemon on your team knows this move.
This is as close to invulnerable as it's possible to be. The only thing you'd realistically have to worry about once you've reached this point is multi-hit attacks, such as Bullet Seed, Rock Blast, etc. There are other ways, but most of them would require your opponent to know beforehand that this was your strategy. For example, an opponent using Knock Off during Hail or Sandstorm, or before using Leech Seed. A Ghost type using Curse would also apply indirect damage. I believe Future Sight is indirect damage? Any Ability tampering by your opponent would also bring your sweeping to an end.
